This invention relates to vision processing, more particularly to a resistive fuse circuit which can be used in a two-dimensional grid to perform image segmentation and smoothing.
One of the first operations performed in early vision processing is smoothing. This has a twofold purpose: first, it reduces noise, which can produce spurious edges, and second, it suppresses fine detail so it will not be detected by an edge detector. The degree to which the image should be smoothed depends on the fineness of detail one wants in the output image. For example, if the observer wants to know the pattern on a striped shirt, a fairly large amount of smoothing should be applied so that the only edges that will be detected correspond to borders between regions of different color. If the observer wants to see the weave of the cloth, very little smoothing should be applied, or the weave will be unobservable. Thus, a device that can perform smoothing at a user adjustable scale is extremely useful.
Smoothing is essentially spatial low-pass filtering, and is usually accomplished by convolving the input image with some band-limited function, often a Gaussian. Digital circuits can obviously perform a convolution, but analog circuits can also perform convolution. In fact, Gaussian convolution is fairly simple to implement in an analog method because of the relation between Gaussian convolution and the diffusion (heat) equation in a two-dimensional sheet. If the intensity distribution of an image is mapped to an infinite sheet in such a way that the initial temperature on the sheet at any point is proportional to the image intensity at the corresponding point in the image, and heat is allowed to diffuse throughout the sheet, the temperature distribution at future times is obtained from the diffusion equation: ##EQU1## where x and y are spatial coordinates, t is time, T(x,y,t) is the temperature distribution at time t, and c is some positive constant. This is exactly the relation that holds if the image is convolved with a Gaussian of variance .sigma..sup.2 =2 ct.
The diffusion equation governs both the diffusion of heat in a sheet and the diffusion of charge in an infinite uniform resistive sheet with uniform distributed capacitance, so they will have the same solution. A discretized, finite version of the infinite sheet can be implemented in analog VLSI by fabricating an array of nodes such that each node connects through resistors to its nearest neighbors and to ground through a capacitor, as Knight did in his optical sensor chip. A one-dimensional example is shown in FIG. 1. The image is stored, perhaps as voltages on capacitors, the light entering the imaging system is shut off, and a resistive-capacitive grid is allowed to relax for a period of time which depends on the degree of smoothing required.
Other methods have been proposed to perform smoothing because the implementation described above does not provide output continuously, which might be inconvenient for later algorithms. One network proposed for continuous smoothing is shown in FIG. 2. The capacitances to ground are replaced by conductances, and the voltage source u.sub.k represents the input image intensity at node k. The equation solved by this resistive-conductive grid is not the diffusion equation, but a discretized version of the equation EQU .gradient..sup.2 y(x)=(y(x)-u(x))/.alpha..sup.2,
where y(x) is the output voltage distribution, u(x) is the input voltage distribution, and the smoothing constant .alpha.=.sqroot.R.sub.v /R.sub.h. An infinite one-dimensional network performs convolution with ##EQU2## instead of e.sup.-x.spsp.2.sup./2.sigma..spsp.2, so the network does not perform Gaussian smoothing. Nevertheless, this network, or a variant, seems to be the usual choice for implementing analog smoothing.
It is important to understand how edges are affected by the resistive grid. Edges can result from boundaries between separate objects or from variations in surface texture or orientation within a single object, and often provide useful information for later algorithms such as image recognition. These edges divide the complete image into several regions. Any linear smoother, such as the resistive grid mentioned above, has no knowledge of where these edges occur and will tend to blur together different regions, making it difficult for later algorithms to find and localize the edge dividing those regions. Mead solves this problem by the use of saturating horizontal resistors, thereby creating a nonlinear smoother. Other proposed solutions based on stochastic arguments and minimization of cost functionals suggest a special type of horizontal resistor (which would replace R.sub.h in FIG. 2) which has the I-V characteristic shown in FIG. 3. Harris (and earlier references within) has also made this suggestion independently. The resistive fuse acts as a normal resistor for small voltages, but fuses and passes little or no current if the voltage across its terminals exceeds a threshold voltage. Since image intensity will presumably be quite different across an edge, the resistive fuse acts as an open circuit and prevents blurring across that edge. A resistive circuit which does exactly that was first developed by Harris, but it requires 33 transistors.